Dirichlet character χ432(227,⋅)\chi_{432}(227,\cdot)

• Label: 432.227
• Modulus: $432$
• Conductor: $432$
• Order: $36$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$432$
Conductor:	$432$
Order:	$36$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 432.bj

$\chi_{432}(11,\cdot)$ $\chi_{432}(59,\cdot)$ $\chi_{432}(83,\cdot)$ $\chi_{432}(131,\cdot)$ $\chi_{432}(155,\cdot)$ $\chi_{432}(203,\cdot)$ $\chi_{432}(227,\cdot)$ $\chi_{432}(275,\cdot)$ $\chi_{432}(299,\cdot)$ $\chi_{432}(347,\cdot)$ $\chi_{432}(371,\cdot)$ $\chi_{432}(419,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{36})$
Fixed field:	36.36.5532004127928253705369187176396364210546696053048780432717505515499814912.1

Values on generators

$(271,325,353)$ → $(-1,-i,e\left(\frac{13}{18}\right))$

First values

$a$	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{ 432 }(227, a)$	$1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{17}{18}\right)$

Gauss sum

Jacobi sum

Kloosterman sum